In January, Johnson announced his plan to file the lawsuit, which aims to prevent members of Congress and their staff from receiving employer contributions to their health care plans. Rep. Jim Sensenbrenner (R-WI) responded to the idea by issuing it a statement calling the lawsuit an "unfortunate political stunt."

A retainer agreement between Johnson's campaign and the Wisconsin Institute for Law & Liberty requires the institute's legal work to be paid for, the Journal Sentinel reported Tuesday, but so far the organization has yet to submit a bill.

“We haven’t sent a bill because, as a public interest firm that normally does not bill or is paid only at the conclusion of a matter, we tend to bill on a longer cycle than a commercial law firm might,” Rick Esenberg, the institute's president, told the newspaper.